This book presents some differential subordination, superordination and sandwich results for analytic functions associated with certain linear operators obtained in the last years. We assume the reader has a good background in univalent and multivalent functions. The book may be of interest to researchers working on differential subordination and superordination. It is a text book giving detailed proofs and illustrative which are intended both for self-help and for courses at graduate levels. The book consists of five chapters organized as follows: In chapter 1, we present the preliminaries and basic concepts that will be needed throughout the book. In chapter 2, we are dealing with classes of non-Bavilević functions involving different operators. In chapter 3, we will give some applications of subordination, superordination of certain subclasses of close-to-convex functions defined by some operators. In chapter 4, we will obtain several inclusion relationships of functions belonging to classes of starlike and convex functions. In chapter 5, we are concerned with subordination-preserving and superordination-preserving properties associated with integral operators.